12v inverter help

Hey, so here's my laptop charger



Here's the 12v inverter I bought



Here's what I got when I opened the box




It all works well until I'm in graphics intense situation and the graphics card starts sucking up the juice. Then the low voltage alarm starts screaming at me (with the engine running).

Would I be better off with the 300W? Or is there a different inverter all together that would be better?

Also, the wire that came with it wasn't long enough so I just used wire from home Reno's that was lying around in the garage. If the inverter is fine to run it and it could be the wire, what wire should I use?

Any help would be greatly appreciated. Cheers.